MHT CET · Physics · Magnetic Effects of Current
A circular arc of radius r carrying current ' \(I\) ' subtends an angle \(\frac{\pi}{8}\) at its entre. The radius of a metal wire is uniform. The magnetic induction at the centre of circular arc is ( \(\mu_0=\) permeability of free space)
- A \(\frac{\mu_0 \mathrm{I}}{8 \mathrm{r}}\)
- B \(\frac{\mu_0 I}{32 r}\)
- C \(\frac{\mu_0 \mathrm{I}}{64 \mathrm{r}}\)
- D \(\frac{\mu_0 \mathrm{I}}{16 \mathrm{r}}\)
Answer & Solution
Correct Answer
(B) \(\frac{\mu_0 I}{32 r}\)
Step-by-step Solution
Detailed explanation
The magnetic induction at the centre of circular arc is
\(B=\frac{\mu_0 I}{4 \pi r} \times \theta\)
\(\therefore \quad B=\frac{\mu_0 \dot{I}}{4 \pi r} \times \frac{\pi}{8} \quad \cdots\left[\because \theta=\frac{\pi}{8}\right]\)
\(\therefore \quad B=\frac{\mu_0 I}{32 r}\)
\(B=\frac{\mu_0 I}{4 \pi r} \times \theta\)
\(\therefore \quad B=\frac{\mu_0 \dot{I}}{4 \pi r} \times \frac{\pi}{8} \quad \cdots\left[\because \theta=\frac{\pi}{8}\right]\)
\(\therefore \quad B=\frac{\mu_0 I}{32 r}\)
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